A high security coding and anti-counterfeiting method based on the nonlinear magnetization response of superparamagnetic nanomaterials

Traditional coding methods based on graphics and digital or magnetic labels have gradually decreased their anti-counterfeiting because of market popularity. This paper presents a new magnetic anti-counterfeiting coding method. This method uses a high-performance coding material, which, along with small changes to the material itself and the particle size of the superparamagnetic nanomaterials, results in a large difference in the nonlinear magnetization response. This method, which adopts 12-site coding and establishes a screening model by measuring the voltage amplitude of 12-site variables, can code different kinds of products, establishing long-term stable coding and decoding means. Through the anti-counterfeiting experiment of wine, the experiment results show that the authenticity of the coded products can be verified using the self-developed magnetic encoding and decoding system. The new coding technology can verify the anti-counterfeiting of 9000 products, with a single detection accuracy of 97% and a detection time of less than one minute. Moreover, this coding method completely depends on the production batch of the superparamagnetic nanomaterials, which is difficult to imitate, and it provides a new coding anti-counterfeiting technology for related industries with a wide range of potential applications.


New coding theory
The paper describes a new anti-counterfeiting method that utilizes the key physical parameters of superparamagnetic nanoparticles nanomaterials and their nonlinear magnetization response characteristics.The method utilizes single magnetic domain size variation, single magnetic domain magnetic moment, and hydrodynamic diameter, and the environmental solution of the MNPs significantly affects their rich harmonic response signals.Hence, they can generate a series of rich and unique password information and implement specific coding and decoding methods for product anti-counterfeiting.

System framework
The paper presents a comprehensive framework for an anti-counterfeiting system specifically designed for highvalue-added products.This framework incorporates various components, such as anti-counterfeiting materials, product marking, anti-counterfeiting technology, product anti-counterfeiting systems, and coding and decoding identification.

Feature 1
The size of MNPs ranges from 5 nm to 10 µm 22 , to ensure their safety in the human body, small MNPs with diameters of less than 50 nm are commonly modified with hydrophilic flexible polymers like Polyethylene glycol (PEG) and dextran, which make them water-soluble and biocompatible.Polymer modifications confer the MNPs with various benefits, such as long-term storage stability, protection against environmental factors, improved dispersion, and enhanced manipulability.Their preparation process inevitably causes each batch of MNP materials to differ in magnetic core particle size or hydrodynamic particle size and Polymer dispersity index (PDI) dispersion.Hence, it is difficult even for manufacturers to imitate MNPs with the same nonlinear magnetization response, MNPs embody extremely high coding security.

Feature 2
Although the hysteresis of MNPs resembles that of a normal magnet, its magnetization response is completely different and it shows a remarkable nonlinear magnetization response characteristic dominated by the Langevin function.This nonlinear magnetization response is influenced by superparamagnetic nanoparticles nanomaterials and their molecular structure, as a special magnetic response force interval, the nonlinear magnetization characteristics of the solution are significantly affected by its environment, hydrodynamic outer diameter, magnetic core particle size, and MNPs shape.Moreover, nonlinear magnetization produces a very rich harmonic signal in addition to the fundamental wave, often the noisiest signal, which is usually discarded.For example, if Direct Current (DC) bias excitation is not applied, the odd harmonic signal (3, 5, 7, and 9) is generated, and even harmonic signals (2, 4, 6, and 8) can be generated when a DC bias excitation is applied.These signals can be saturated at a high magnetic field strength.Because of the relaxation time described below, real and imaginary part responses have different component proportions, depending on the conditions.This series of magnetized harmonic signals from each harmonic can provide a lot of coding information for MNPs.The coded information, with small changes, such as a change in the solution's viscosity or a particle size bias of 2 nm, produces a significant difference in magnetization response.Therefore, multi-bit data can be coded based on the relevant characteristics.

Feature 3
When compared with other magnetic marker materials, MNPs exhibit a greater magnetization response, which makes them highly suitable for eigenvalue extraction.A greater magnetization response characteristic makes MNPs ideal for archival storage purposes.Moreover, MNPs possess excellent physical stability, which ensures high sensitivity and analysis accuracy, while expanding detection range.Hence, MNPs with superparamagnetic properties are chosen as marker materials for product anti-counterfeiting testing.The unique properties of MNPs make them promising materials for anti-counterfeiting and traceability applications, and they offer reliable code material for combatting counterfeiting in various products.

Relaxation time
The relaxation phenomenon is a dynamic response property of MNPs.At the microscopic level, the structural changes of MNPs can be reflected in macroscopic magnetic signals by changes in relaxation time.In MNP sample solutions, the Neal 23 relaxation time is commonly expressed: In the equation, the characteristic time, is usually taken as τ 0 = 10 −9 s , d c is the inner diameter of the magnetic core, and K is the magnetic anisotropy constant.
Brownian 24 relaxation time is commonly expressed: where η is the viscosity of the carrier solution (taking 1 mPa of pure water), V H is the hydrodynamic volume of surface-modified MNPs: d H is the hydrodynamic diameter of surface-modified MNPs, and K B T is the thermal energy (K B : Boltzmann constant, T: absolute temperature).The characteristic time 25 , τ eff , is the effective relaxation time and is given by the following equations: The relaxation time determines how quickly MNPs return to their initial state after being magnetized.A smaller relaxation time implies faster recovery, which enables the MNPs to exhibit a more rapid response to (1) Due to the rich magnetic response signals of its MNPs, an MNP sample from Nanoeast (Nanjing Biotechnology Co., Ltd., China) (inner diameter: 30 nm) was selected, and 0.1 mL of the sample was diluted with 0.4 mL of PBS.Next, 0.1 mL of the diluted sample was transferred into a new sample bottle.The excitation magnetic field strength of the automatic coding and decoding detection system was set at millitesla (mT).As shown in Fig. 1, the signal peaked at around 1 kHz and then decreased rapidly with increasing frequency.To ensure that the signal could be obtained with small particle sizes and to improve the signal-to-noise ratio, subsequent experiments were done at 1 kHz as the actual excitation frequency.Figure 1 shows the third harmonic signal amplitude of the MNPs at different frequencies.

Harmonic characteristics of MNPs
Because of the unique magnetic core structure and highly non-linear AC magnetization response of MNPs, it is difficult to effectively acquire their characteristic signals using conventional linear magnetization measurement methods 25 .To overcome this challenge, a dual-frequency AC excitation approach is employed, whereby MNPs are excited by simultaneously applying two alternating magnetic fields with different frequencies, so that higherorder harmonic signals are excited, and the odd harmonic signals are collected and analyzed.By analyzing these odd harmonic signals, the magnetization characteristics of MNPs can be measured more accurately.Moreover, because this method offers high signal stability and anti-interference capability, it is suitable for non-contact magnetization characterization during product anti-counterfeiting testing.A new anti-counterfeiting method demonstrates reliability and robustness in complex environments and provides effective technical support for product authentication and traceability.The magnetization characteristics of MNPs can be expressed as follows, using the Langevin function 26 .
where m is the magnetic moment of the magnetic core, K B is the Boltzmann constant, T is the absolute temperature, and µ 0 is the vacuum's permeability.Under the action of an external magnetic field, the magnetization, M, of MNPs can be expressed 27

as follows:
where M S is saturation magnetization, m 0 is the magnetic moment, µ 0 is vacuum permeability, H (t) is the applied magnetic field, K B is the Boltzmann constant, T is the Kelvin temperature, and L( ) is the langevin function.An excitation field with an excitation strength, H(t), is applied externally to the MNPs and it can be expressed as follows: where f 1 is the frequency of the high-frequency excitation field, A 1 is the initial amplitude of the high-frequency excitation field, t 1 is the time, θ 1 is phase angle, f 2 is the frequency of the low-frequency excitation field, A 2 is the amplitude of the low-frequency excitation field, t 2 is the time, and θ 2 is the phase angle.
A non-linear magnetization response contains higher harmonics, which are integral multiples of the frequency of the external excitation field (i.e., k = 1, 2, 3…).By extending the right side of Eq. ( 8) in a Fourier series, the kth harmonic signal (odd harmonic signal) from the MNPs can be obtained 28 using the following equation: www.nature.com/scientificreports/ The real part and the imaginary part of alternating current (AC) susceptibility can be calculated using the Debye model and the Fokk-Planck function.The real part of AC magnetic susceptibility generally tends to decrease with increasing excitation frequency.When the excitation frequency is < 1 kHz, the real part of the AC magnetic susceptibility decreases slowly.When the excitation frequency exceeds 1 kHz, the real part of the exchange susceptibility rate begins to decline rapidly, while the virtual part peaks at particular frequency from 1 to 5 kHz.When the excitation frequency exceeds the peak frequency, the virtual part of the AC susceptibility begins to decrease.Because of the wide variation range of the real and imaginary parts, the product can be coded using the trends of the real and imaginary parts of the AC magnetic susceptibility.
The analysis of the characteristics of the harmonic signals generated by MNPs under an excitation magnetic field of 7 mT 29 was derived and verified using Eq.(11).Analysis of the harmonic signals generated by MNPs at an excitation magnetic field of 7 mT indicates that the amplitude of the odd harmonics increases with sample volume, while the amplitude of each odd harmonic decreases with an increase in the number of harmonic decompositions.This unique trend suggests that the magnetic response signal of higher harmonics is smaller than that of lower harmonics.MNPs can be used to code products based on their magnetic response properties.MNPs can exhibit unique magnetic signatures that are unaffected by changes in the external environment.Using the odd harmonic signals generated by MNPs, it is possible to create distinctive and specific coding data for different products, allowing for reliable and accurate product identification, even in varying conditions.Figure 2 shows the odd harmonic characteristics of MNPs.
Customized Nanoeast (inner diameter: 25 nm), Resovist (Fujifilm, Japan) (inner diameter: 30 nm) and Ocean (Nanotech USA) (inner diameter: 30 nm) magnetic MNPs were used as samples.Six different MNP solutions were prepared.Samples A and B are composed of MNPs from Nanoeast and carboxyl group, which are two samples with different hydrodynamic diametric diameter.Samples C and D are composed of MNPs from Resovist and carboxyl group, which are two samples with different hydrodynamic diametric diameter.Samples E and F are composed of MNPs from Ocean and dextran, which are two samples with different hydrodynamic diametric diameter.
Figures 3 and 4 show the harmonic signal ratios and the harmonic signals of the MNPs, respectively.The data in Figs. 3 and 4 show that under the same harmonics, different kinds of MNP solutions produce different signal values.Even for the same MNP solution, the harmonic signal amplitude differs because of small differences in magnetic particle sizes.Because relatively high MNP concentrations affect the spacing between ions in aqueous solution environments, a lower concentration environment causes ions to be more spaced out, allowing the random motions between ions to collide.The probability of van der Waals forces causing ions to unite increases at high concentrations and decreases at low concentrations.Relative to the actual response to ion dispersion, rather than the results measured by Particle size analyzer, different of the concentration will also affect the magnetic response signal.This difference provides a unique "fingerprint" for the product.Therefore, because of differences in various factors, including MNP kinds, coating layers, and magnetic core particle size, the MNP magnetic response behavior differs under a magnetic field, which provides a rich data source for coding.

Particle size and material composition of MNPs
The coding method proposed in this paper uses MNPs as high performance coding materials.There are many kinds of magnetic materials, Fe 3 O 4 is one of the most widely used, its particle size distribution is about 1-100 The harmonic characteristics of MNPs.nm.When the particle size of MNPs is 30 nm, with the further reduction of particle size, MNPs exhibit superparamagnetic properties.It has strong magnetism under the external magnetic field, but the magnetism will disappear quickly after the exclusion of the magnetic field.MNPs with smaller particle size have faster magnetic response and stability, when the particle size of MNPs is larger than 30 nm, the response speed is slower but the magnetic response signal is stronger.Second, MNPs can be surface-modified, bring in a layer of polymer (e.g., polyvinyl alcohol, polyacrylic acid, gelatin, etc.).Hydrophilic groups or oleophilic groups (-CHO, -OH, -SH, -COOH, -NH 2 , etc.) or MNPs can be combined with proteins, enzymes, vitamins, DNA and other bioactive substances.These methods can regulate the chemical stability and dispersion of MNPs.The magnetic properties of MNPs can be regulated by different surface modification methods, which can provide rich coding information for MNPs material coding.

The developed magnetic encoding and decoding system
The developed magnetic encoding and decoding system based on MNP materials has high sensitivity and reliability and can trace the whole process of high-value-added products.The system's core parts are the pickup coil and excitation device, and the coded signal is processed and reconstructed by a signal processing unit and host  www.nature.com/scientificreports/computer unit.The differential pickup coil 26 makes the excitation field to form a balanced state in the pickup coil, reduces fundamental frequency interference, and can detect weak magnetic nanoteslas nT-level signals.
The system uses Helmhertz coils 30 to generate a high-frequency magnetic field and a cylindrical coil to generate a low-frequency magnetic field, which plays a role in improving magnetic field intensity.Moreover, the upper computer unit can measure and reconstruct odd and even harmonic signals using in-house program, and a magnetic shield device is used to prevent interference from the environmental magnetic field.Figure 5 show a schematic diagram of the developed magnetic encoding and decoding system.

Coding module
The coding principle Based on product anti-counterfeiting requirements, the harmonic voltage amplitude of different types of MNPs, the ratio of each harmonic voltage amplitude, and the harmonic voltage amplitude of the mixed solution of MNPs are used to determine whether the product is coded, based on the following coding principle.S 1 : Different kinds of MNPs are selected based on the demand and prepared into anti-counterfeiting labels.Various magnetic response properties are obtained by adjusting various MNP parameters, such as the coating layer, shape, particle size, and the type of target coupling protein of the MNPs.S 2 : Preparatory experiments are carried out on the products that need to be traced back to measure their harmonic voltage amplitude, the ratio of odd harmonic voltage amplitude, and the magnetic response signals of the mixed solution of MNPs.These data can be measured using the in-house automatic compilation code recognition system, with the results determining the value of each coding data site.To ensure each product has unique coding data, the number of coding sites can be set to 12 or several of the 12 coding data sites in the coding process.S 3 : The coded information for each product is stored in the product coding database, allowing for comparison during product anti-counterfeiting validation.S 4 : In product anti-counterfeiting involves measuring the harmonic voltage amplitude of various types of MNPs, the ratio of odd harmonic voltage amplitude, the harmonic voltage amplitude of MNPs with functionalized surface coating, and the harmonic voltage amplitude of mixed solutions of various types of MNPs.S 5 : These measurements are then compared with the data in the product coding database to establish each data site's consistency with the corresponding data sites in the coding database.If deviation is detected, it is necessary to establish if it falls within an acceptable range and if it does, if the product passes anti-counterfeiting verification.However, a deviation that exceeds the acceptable range may indicate problematic or counterfeit products.Figure 6 shows the coding principle.

Coding method
A mixed solution of different types of MNPs When different types of MNPs or MNPs with different coatings are mixed at various ratios 31 (1:1, 1:3, 1:6, and 1:9), they experience mutual gravitation and repulsive forces that cause them to agglomerate in the solution, agglomeration increases MNP particle size and changes their relaxation time, which affects the magnetic response signal generated by the mixed solution.Notably, the magnetic response signal of a mixed solution differs from that of a solution with two types of MNPs only.Mixing two types of MNP solutions at different proportions can generate different harmonic signals for product coding.Therefore, the harmonic signals of MNPs mixed with other MNP types or MNPs with different coatings can be used as a parameter for coding products.

MNPs with functionalized surface coating
The surface of the magnetic cores is coated with hydrophilic materials 32 like oleic acid, which can prevent magnetic core aggregation and impart hydrophilic properties to the MNPs.Additionally, modifying the outer layer of the hydrophilic shell can achieve MNP binding to various functional target proteins or molecules using chemical bonds or biological proteins with coupling functions, this produces a range of MNPs with different harmonic signals.Particle size changes before and after coupling MNPs with the target protein affect the relaxation time www.nature.com/scientificreports/ of the MNPs and the magnetic response signal.Coupling the targeted proteins with MNPs generates unique magnetic response signals, and changing the target protein type achieves diverse MNP magnetic response signals.Hence, the harmonic signals of MNPs modified with functionalized surface coating can be used as coding parameters for product coding purposes.

Odd and even harmonic components
The study employed a coding approach based on the odd and even harmonic signals of the MNP solutions for product coding 33 .Specifically, the 2nd, 3rd, 4th, 5th, 7th, and 9th harmonic signals of the MNPs were used as coding data sites.Each harmonic signal exhibits unique magnetic response characteristics, ensuring coding distinctiveness.The odd harmonic signal ratio is calculated by dividing the amplitude of the 9th harmonic signal by the amplitude of the 3rd harmonic signal, resulting in the ratios, 9/3, 7/3, 5/3, 7/5, 9/5, and 9/7, measuring these signal ratios generates six independent coded data sites.Using this coding technique, we achieved reliable product coding using the magnetic response signals of the harmonic components of the MNPs as coding parameters.Figure 7 shows the code sites.

Screening model
To generate nonlinear magnetic response signals by magnetizing MNPs in the excitation device, which are collected by the pickup coil.Isolation amplifiers are used to filter and amplify signals to ensure data quality and reliability.The voltage amplitude of odd-order and even-order harmonic signal and the magnetic response signal of MNPs are obtained by using a phase-locked amplifier.The screening model was constructed with LabVIEW, the logic comparison module and the mathematical operation module were used to calculate the odd harmonic signal ratio, and the difference between the measured data and the database data was compared to determine its consistency.A threshold or tolerance range of ± 3% is set to determine whether the deviation between the measured data and the encoded database data is within an acceptable range.The logical judgment module of LabVIEW is used to make a logical comparison between the comparison result and the set threshold value.The results of logical judgment are integrated, and the screening model is realized by the logical structure of LabVIEW.According to the result of model judgment, the anti-counterfeiting verification of the product is carried out.If the measurement data is consistent with the coded database data and the deviation is within ± 3%, the product passes the verification; Otherwise, there may be problems or shoddy products that need further treatment or inspection.According to the verification results, the LabVIEW program gives the corresponding feedback information, displays the prompt of passing or failing the verification, and records the verification results for subsequent reference.

Decoding module
The system setup shown in Fig. 5 was used to construct the detection platform for the identification system to enable product coding detection and anti-counterfeiting.In the experiment, the MNP sample was magnetized using a mixing AC magnetic field (model: NF4610, NF4620), and the magnetic response signal of the MNPs was collected by a pickup coil.The magnetic signal was then converted into an electrical signal by a resonant circuit, an isolation amplifier (model: NF5325), and a phase-locked amplifier (model: NF5645).Electrical signals were then transferred to a personal computer for processing, analysis, and storage using LabVIEW software.The entire process of detecting the magnetic response signal takes less than a minute.
To validate the proposed method, determine its feasibility, and improve detection efficiency, magnetic field intensity was screened.Next, each coding method was tested to verify that the harmonic amplitudes generated  the sample was diluted in 0.4 mL of PBS.Next, 0.1 mL of the diluted sample D was transferred into four sample bottles, whereas 0.1, 0.3, 0.6, and 0.9 mL of the diluted sample F were transferred into separate sample bottles.
The automatic coding and decoding detection system was then used to apply an excitation magnetic field strength of 4 mT (frequency: 1 kHz) to the MNP samples, and their harmonic signal amplitudes were measured using the system.This indicates that signal amplitudes do not significantly correlate between the mixed solutions and the signal amplitudes of the respective solutions of the two types of MNPs.Table 4 shows the coding information of the different kinds of mixed MNP solutions.

Code site: MNPs with the functionalized surface coating
The difference in the signal values of the MNP solutions modified with various chemical bonds or proteins was assessed.Sample D (inner diameter: 30 nm) MNPs were mixed with 0.9% saline or lipase, to obtain MNPs that produced different harmonic signals, and the magnetic signal amplitude of the two combined solutions was measured at the 3rd harmonic.The experiment was repeated thrice, calculating the average amplitude of the three measurements of harmonic amplitudes to obtain the coded sites.This analysis showed that there was a difference but no correlation between the signal amplitudes of the solutions of MNPs modified with various chemical bonds or proteins.Table 5 shows the coding information of the MNPs with functionalized surface coatings.

MNP stability analysis
Sample D (0.1 mL) was diluted with 0.4mL PBS, followed by the transfer of 0.1 mL of the resulting solution to a sample vial and the addition of 10 µL of a Proclin300 (AbMole, USA) preservative, the magnetic signal amplitude is measured at the third harmonic.The experiments were repeated thrice a week for two months.The experimental results show that the signal amplitude ranged between 0.09 and 0.1 mV and the signal deviation range was within 0.02%, minimal MNP signal fluctuation over the two months of testing, the coded material can be used for long-term storage without significant degradation or changes in magnetic signal properties.Figure 8 shows the amplitude of 3rd harmonic signals during the MNP stability analysis.The coding sites of various types of MNPs and their corresponding odd and even harmonics signals were thoroughly investigated.Additionally, solutions containing different types of MNPs mixed at specific proportions and MNPs with functionalized surface coating were also examined.These analyses revealed distinct magnetic response signal amplitudes at each coding site.These signal values represent independent datasets without correlation.Using the coding principle and method described earlier, the number of variation parameters per code site can be multiplied to determine the number of possible coded products.The current study, the research has achieved 9000 different coded products.However, the number of products that can be coded is limited by the low number of available coding sites.To overcome this limitation, further research is needed to identify methods of increasing the number of coding data sites and expanding the number of coded products to beyond 10,000.Other approaches to enhancing coding capacity could involve optimizing the coding algorithm or improving the MNP Table 3.The coding information of the magnetic signal from a magnetic sphere under the 2nd and 4th harmonics.www.nature.com/scientificreports/preparation process, which may expand coding capacity without necessarily increasing the number of coding sites.Figure 9 shows the automatic coding and decoding detection system's coding data acquisition interface.

The stability of the interference state
It is very important for improving the practical value of our research.The effects of main environmental interferences to superparamagnetic material and its magnetic measurement including temperature, humidity and electromagnetic interference are discussed additionally.

Temperature effect
The magnetic properties of MNPs may be affected by the change of ambient temperature during practical application, because the superparamagnetism of MNPs is a very special property that the thermal energy exceeds the magnetic anisotropy barrier.Therefore, the temperature is a critical interference factor that may affects the stability of the developed magnetic coding and decoding system.
As the example of temperature interference, MNP sample D (0.1 mL) was diluted with 0.4mL PBS, and separated to four same sample bottles (0.1 mL diluted sample in each bottle).Four samples were heated to 25 °C, 30 °C, 35 °C and 40 °C in air heating bathtub, respectively, and then measured immediately using the developed magnetic coding and decoding system.The excitation field and frequency were fixed at 4 mT and 1 kHz, as well as the fixed humidity and electromagnetic interference for each measurement.
All sample measurements were repeated for three times, the mean amplitude of each odd harmonic and harmonic ratio were shown in Fig. 10, respectively.
The experimental results show that the harmonic response of the MNP changes with different temperatures.We think the change in harmonic amplitude was due to the higher thermal energy and faster relaxation time.Comparing to the harmonic amplitude, the harmonic ratio gives a much better stability, because the temperature variation was cancel out by proportional calculation.The maximum change in harmonic ratio was about 2% (9/7), and the average was less than 1% in all other different temperature cases.Moreover, the change in harmonic amplitude was computable and predictable due to its monotonic variation with temperature.It means we can calculate the accurate signal by introduce a simple temperature measurement and feedback system if the original harmonic amplitude signal is necessary in coding and decoding.

Humidity effect
Humidity is another factor that may affect the properties and stability of MNPs.In the humidity interference experiment, two MNP samples were prepared in the same process of temperature case except heating.Two of the samples were placed in vacuum bottle (humidity about 0%), and other two samples were placed in 90% relative humidity environment (produced by water vapor) at room temperature.All samples were measured three times using the developed magnetic coding and decoding system (total six measurements for vacuum and 90% humidity, respectively), and the mean amplitude of each odd harmonic component and calculated harmonic ratio were shown in Fig. 11, respectively.
The experimental results show that the humidity does not affect either the harmonic amplitude or calculated harmonic ratio.We obtained good stability in severe environment humidity changes.
Figure 10.The mean amplitude of each odd harmonic and harmonic ratio of MNPs affected by environment temperature.

Electromagnetic interference
Electromagnetic interference may affect the properties of MNPs, as well as the stability of the system.In the electromagnetic interference experiment, one MNP sample was prepared same to the temperature interference case except heating process (take one sample bottle instead of four).We thought that the main electromagnetic interference in nature environment was the power frequency (50 or 60 Hz), thus, the electromagnetic interference was produced by a pair of Helmholtz coil with a frequency of 50 Hz and a strength of 4 mT.The Helmholtz coil pair was set nearby the sample detection area, and then the mean amplitude of each odd harmonic and harmonic ratio were recorded in Fig. 12 with and without interference.
The experimental results show that the outer electromagnetic field affects the detection result very slightly.The maximum change in harmonic ratio was about 2% (9/7), and the average was less than 1% in all other cases including harmonic amplitude and ratio.We thought the slight change in harmonic ratio was mainly due to the frequency multiplication between 50 Hz (interference) and 1000 Hz (excitation field), which may cause some interference in signal to noise ratio (SNR).An adjustment of excitation frequency, such as 1000 to 1020 Hz, will be effective in further reducing of environmental electromagnetic interference.Moreover, the mixture of the low and high frequency excitation field may cause some more complex magnetization.For example, we can  earn some harmonic components in 1000 ± 100 Hz and 1000 ± 200 Hz, which may contribute more encodable magnetizations.However, we can obtain good stability in severe environment electromagnetic interference.
As a shot summary, usual environmental interferences within the scope of daily life do not affect the stability of the MNPs and measurement system significantly or can be compensated easily.We think the developed magnetic coding and decoding system was suitable in a large number of daily scenes.

Strong magnetic field
In theory, superparamagnetic nanoparticles should lose their magnetization due to the thermal energy and very fast Brownian or Neel relaxation time if the external magnetic field is moved out.However, there is always some small remanence in large nanoparticles with high magnetic moment that suitable for AC magnetization measurement.A typical application of this remanence is named magnetic hyperthermia.In this paper, we measured the signal stability of the MNPs before and after a strong magnetization to confirm the influence of the external magnetization that may be difficult to avoid in daily life.The magnetic interference field was produced by a NdFeB magnet with a surface magnetic field of 450 mT.0.1 mL of MNP sample D diluted by 5 times in PBS solution was used for further experiment.The strength and frequency of the measurement excitation field was 4 mT and 1000 Hz, respectively.The MNPs sample was placed beside the NdFeB magnet for 10 min for magnetization.The odd harmonic components and calculated harmonic ratios before and after NdFeB magnetization were recorded in Fig. 13.The experiment was performed three times and the mean amplitude was final record to reduce the measurement error.
The experimental results show that the magnetization due to the NdFeB magnet affected the detection stability very slightly.The maximum change in harmonic ratio was about 2% (9/7), and the average was less than 1% in all other cases including harmonic amplitude and ratio.We thought the slight change in harmonic ratio 9/7 was due to the small harmonic response strength and measurement error but not the NdFeB magnetization, because all other measurement results were very stable.We think the stability of the MNPs sample to external magnetization was due to the small core and hydrodynamic size of the nanoparticle, but may become severe for particles larger than 30 nm core diameter.As a shot summary, we think the interference from external strong magnetic field do not affects the stability of the MNP in current developed system significantly.However, we should still avoid being too close to other magnetic fields during the measurement, as it can affect the non-linear magnetization response even saturate the MNPs sample.

Information management
Product anti-counterfeiting involves the following segments: production, processing, coding, circulation, and restoration.Production involves capturing fundamental product information related to the production process and other critical details.This information helps establish a product's authenticity and traceability.In the processing stage, high-value-added products are preserved and packaged, and important data like the production date, batch number, location, processing details, and logistics information are recorded.These records are important for maintaining product integrity throughout the supply chain.In coding, MNPs are used in the anti-counterfeiting labels or marks added to products.Coding enhances product security and protection against counterfeiting.During circulation, coded products are transported and sold through the distribution process, with movement across various channels until they reach the end user.Restoration involves using the developed magnetic encoding and decoding system to extract coded information from the MNP-containing anti-counterfeiting marks.This information is then compared with the coding database to verify product authenticity.The anti-counterfeiting Figure 13.The mean amplitude of each odd harmonic and harmonic ratio of MNPs affected by NdFeB magnetization.
code database serves as a repository of detailed product information.As the number of coded products increases, the database is regularly updated to maintain data accuracy and completeness.Using network technology, the anti-counterfeiting code database can synchronize and share real-time data with each segment's information systems.Consumers can scan product codes or manually enter them to access various information, including production details and distribution networks.Figure 14 illustrates the anti-counterfeiting coding database.

Anti-counterfeiting theory
Wine anti-counterfeiting is an important task 34 .We adopted the coding method based on the MNPs studied.Using a 12-code sites and experimental data, we established the magnetic code information for wine and used the developed magnetic encoding and decoding system to measure the amplitudes of the odd and even harmonic signals of wine samples containing MNP anti-counterfeiting marks 35 .The magnetic code information of each coding site was then verified individually, measuring the magnetic response signal and verifying the coded data can accurately determine the wine's identity and offer a strong product guarantee to consumers.

Anti-counterfeiting analysis
Calibration of the automatic coding and decoding detection system is a key step to ensure the accuracy of the experiment.Calibrate the excitation magnetic field intensity, eliminate the variable factors in the experiment, and ensure the uniformity of experimental conditions, repeated experiments can help confirm the stability and repeatability of the results.By calculating the mean and standard deviation of the experimental results, the consistency and stability of the experiment can be evaluated, so as to improve the reliability of the results.
Analyze the following steps to create wine anti-counterfeiting labels using MNPs.
(2) From the diluted sample, 0.1 mL was used to create the first anti-counterfeit label using the laser method.

Comparative analysis
Traditional anti-counterfeiting methods mainly use stable isotopes to achieve product traceability.Due to the extremely low content of stable isotopes, their content is usually detected by mass spectrometers.Table 6 shows the mass spectrometer test process 37,38 .Superparamagnetic nanoparticles are used as high performance coding materials to judge the authenticity of the samples by the self-developed automatic coding and decoding recognition system.Table 7 shows the detection process based on superparamagnetic nanomaterials coding technology.
As can be seen from Tables 6 and 7, the use of superparamagnetic nanoparticles as high-performance coding materials has more advantages than traditional isotope detection methods in terms of detection process and detection time, and the detection process does not require professional personnel to operate.
In terms of cost, the price of isotope mass spectrometers varies by model, brand, performance, and configuration, ranging from tens of thousands of dollars to millions of dollars.The superparamagnetic nanomaterial coding technology is relatively economical, and the detection cost of each product to be tested is within $1.In addition to the daily maintenance of the instrument, the isotope mass spectrometer also needs to consider the maintenance cost of the peripheral part, and the maintenance cost of the automatic encoding and decoding recognition system based on superparamagnetic nanomaterials is mainly focused on the daily maintenance and use of the instrument itself, and the cost is relatively low.Automatic coding and decoding detection systems based on superparamagnetic nanomaterials do not require additional training and are relatively simple to operate, while isotopic mass spectrometry rules require systematic training, which may add additional cost and time investment.
The encoding technology based on superparamagnetic nanoparticle materials uses the magnetic properties of magnetic nanoparticles to store information, and realizes the storage of single or multi-value information by adjusting the magnetic moment size, direction and other parameters.Due to the small size and high information density of magnetic nanoparticles, efficient information storage and management can be achieved at the micro scale.The combination of particle size, shape and magnetic properties is flexible to meet different product coding requirements, so its storage capacity and performance are relatively high.In contrast, stable isotope coding takes advantage of the special properties of isotopes.Although 274 stable isotopes have been found, the main applications are still a few, such as deuterium, carbon-13, nitrogen-15 and so on.As a result, its storage capacity is relatively low due to isotope type and quantity limitations.
In general, superparamagnetic nanoparticle coding technology has significant advantages in terms of information storage capacity and flexibility, as well as maintenance costs and personnel training.

Future directions
The coding technique based on superparamagnetic nanomaterials proposed in this paper is applied to other industries.For example, in the pharmaceutical industry, magnetic nanoparticles are added to drugs to ensure the authenticity and safety of drugs, prevent counterfeit drugs from entering the market, and ensure the safety of patients.In the food industry, by adding magnetic nanoparticle materials to food packaging or labels, food information can be recorded and traced to improve food safety.In the retail industry, the realization of smart retail and personalized recommendations can enhance the consumer shopping experience by scanning the magnetic nanoparticle encoded information of products.In the agricultural products industry, an information traceability platform based on magnetic nanoparticle coding can be established to achieve the entire information record and query from production to sales, and improve the quality and safety of agricultural products.It can also be combined with artificial intelligence and big data technology to achieve intelligent management and data analysis of coded products, and improve the anti-counterfeiting effect and management level 39,40 .

Detection procedure
Step description Detection time

Sample preparation
Place the product under test with the magnetic nanoparticle label into the testing instrument 1 min Product testing The magnetic information of the magnetic nanoparticle material is automatically detected and analyzed by the detector based on the 12-site coded data

Report results
Reports in the form of testing the authenticity of products

Figure 1 .
Figure1.The relationship between signal amplitude and magnetic field frequency.

Figure 3 .
Figure 3.The harmonic signal ratio of MNPs.

Figure 4 .
Figure 4.The harmonic signals of MNPs.The data show that under the same harmonic, the magnetic response signals of different types and concentrations of MNP solutions differ and the signals are unique.

Figure 5 .
Figure 5.A schematic diagram of the developed magnetic encoding and decoding system.

Figure 6 .
Figure 6.Flowchart of the coding principle.S 1 : MNP preparation.S 2 : carry out coding tests on products based on the coding principles.S 3 : enter coded data into the database.S 4 : carry out decoding tests according to decoding principles.S 5 : anti-counterfeiting tests.

Figure 7 .
Figure 7. Code sites.The meaning of the coded data for each coding site is shown.

Figure 8 .
Figure 8. MNP stability analysis confirmed that the magnetic properties of the MNPs were stable and that they could be used as long-term anti-counterfeiting coding materials.

Figure 9 .
Figure 9. Product coding and decoding information interface diagram.

Figure 11 .
Figure 11.The mean amplitude of each odd harmonic and harmonic ratio of MNPs affected by environment humidity.

Figure 12 .
Figure 12.The mean amplitude of each odd harmonic and harmonic ratio of MNPs affected by environment electromagnetic.

Table 1 .
The coding information of different types of MNPs.

Table 2 .
The coding information of the magnetic signal from a magnetic sphere under the 3rd, 5th, 7th, and 9th harmonics.

Table 4 .
The coding information for the mixed solutions of different types of MNPs.

Table 5 .
The coding information of the MNPs with functionalized surface coating.

Table 6 .
Mass spectrometer test process.Sample injectionIt is injected into the mass spectrometer in gaseous, liquid or solid formIonizeThe molecules or atoms in the sample are ionized, in the process of ionization, the molecules or atoms in the sample lose or gain electrons, forming charged ionsMass spectrometryThe test is carried out in the detector of the mass spectrometerData analysisThe resulting data is presented in the form of mass spectrograms

Table 7 .
The detection process based on superparamagnetic nanomaterials coding technology.